We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation.We prove the existence theorems for both the con...We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation.We prove the existence theorems for both the convex and nonconvex problems.We also show the existence of extremal periodic solutions and provide a strong relaxation theorem.Finally,we provide an application to nonlinear periodic control systems.展开更多
In this paper, some iterative schemes for approximating the common element of the set of zero points of maximal monotone operators and the set of fixed points of relatively nonexpansive mappings in a real uniformly sm...In this paper, some iterative schemes for approximating the common element of the set of zero points of maximal monotone operators and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed. Some strong convergence theorems are obtained, to extend the previous work.展开更多
A proximal iterative algorithm for the mulitivalue operator equation 0 ∈ T(x) is presented, where T is a maximal monotone operator. It is an improvement of the proximal point algorithm as well know. The convergence o...A proximal iterative algorithm for the mulitivalue operator equation 0 ∈ T(x) is presented, where T is a maximal monotone operator. It is an improvement of the proximal point algorithm as well know. The convergence of the algorithm is discussed and all example is given.展开更多
In this paper, some new iterative schemes for approximating the common element of the set of fixed points of strongly relatively nonexpansive mappings and the set of zero points of maximal monotone operators in a real...In this paper, some new iterative schemes for approximating the common element of the set of fixed points of strongly relatively nonexpansive mappings and the set of zero points of maximal monotone operators in a real uniformly smooth and uniformly convex Banach space are proposed. Some weak convergence theorems are obtained, which extend and complement some previous work.展开更多
In order to find roots of maximal monotone operators, this paper introduces and studies the modified approximate proximal point algorithm with an error sequence {e k} such that || ek || \leqslant hk || xk - [(x)\tilde...In order to find roots of maximal monotone operators, this paper introduces and studies the modified approximate proximal point algorithm with an error sequence {e k} such that || ek || \leqslant hk || xk - [(x)\tilde]k ||\left\| { e^k } \right\| \leqslant \eta _k \left\| { x^k - \tilde x^k } \right\| with ?k = 0¥ ( hk - 1 ) < + ¥\sum\limits_{k = 0}^\infty {\left( {\eta _k - 1} \right)} and infk \geqslant 0 hk = m\geqslant 1\mathop {\inf }\limits_{k \geqslant 0} \eta _k = \mu \geqslant 1 . Here, the restrictions on {η k} are very different from the ones on {η k}, given by He et al (Science in China Ser. A, 2002, 32 (11): 1026–1032.) that supk \geqslant 0 hk = v < 1\mathop {\sup }\limits_{k \geqslant 0} \eta _k = v . Moreover, the characteristic conditions of the convergence of the modified approximate proximal point algorithm are presented by virtue of the new technique very different from the ones given by He et al.展开更多
By using the perturbation theories on sums of ranges for nonlinear accretive mappings of Calvert and Gupta (1978),the abstract result on the existence of a solution u ∈ L^p (Ω) to nonlinear equations involving p...By using the perturbation theories on sums of ranges for nonlinear accretive mappings of Calvert and Gupta (1978),the abstract result on the existence of a solution u ∈ L^p (Ω) to nonlinear equations involving p-Laplacian operator △p, where 2N/N+1〈p〈+∞ and N (≥ 1 ) denotes the dimension of R^N,is studied. The equation discussed and the methods shown in the paper are continuation and complement to the corresponding results of Li and Zhen's previous papers. To obtain the result ,some new techniques are used.展开更多
In this paper, two iterative schemes for approximating common element of the set of zero points of maximal monotone operators and the set of fixed points of a kind of generalized nonexpansive mappings in a real unifor...In this paper, two iterative schemes for approximating common element of the set of zero points of maximal monotone operators and the set of fixed points of a kind of generalized nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed. Two strong convergence theorems are obtained and their applications on finding the minimizer of a kind of convex functional are discussed, which extend some previous work.展开更多
A new projection scheme with errors for zero points of maximal monotone operators is introduced and is proved to be strongly convergent to zero points of maximal monotone operators in Banach space by using the techniq...A new projection scheme with errors for zero points of maximal monotone operators is introduced and is proved to be strongly convergent to zero points of maximal monotone operators in Banach space by using the techniques of Lyapunov functional and generalized projection operator, etc.展开更多
In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operato...In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operators. We establish the existence and uniqueness ofanti-periodic solutions, which improve andgeneralize the results that have been obtained. Finally weillustrate the abstract theory by discussing a simple example of an anti-periodic problem fornonlinear partial differential equations.展开更多
By using the perturbation results of sums of ranges of accretive mappings of Calvert and Gupta(1978),the abstract results on the existence of solutions of a family of nonlinear boundary value problems in L2(Ω) are st...By using the perturbation results of sums of ranges of accretive mappings of Calvert and Gupta(1978),the abstract results on the existence of solutions of a family of nonlinear boundary value problems in L2(Ω) are studied.The equation discussed in this paper and the methods used here are extension and complement to the corresponding results of Wei Li and He Zhen's previous papers.Especially,some new techniques are used in this paper.展开更多
This paper uses a hybrid algorithm to find a common element of the set of solutions to a generalized mixed equilibrium problem, the set of solutions to variational inequality problems, and the set of common fixed poin...This paper uses a hybrid algorithm to find a common element of the set of solutions to a generalized mixed equilibrium problem, the set of solutions to variational inequality problems, and the set of common fixed points for a finite family of quasi-C- nonexpansive mappings in a uniformly smooth and strictly convex Banach space. As applications, we utilize our results to study the optimization problem. It shows that our results improve and extend the corresponding results announced by many others recently.展开更多
One parabolic p-Laplacian-like differential equation with mixed boundaries is au/at in the corresponding studies is replaced by a(au/at), studied in this paper, where the item au/at which makes it more general. The...One parabolic p-Laplacian-like differential equation with mixed boundaries is au/at in the corresponding studies is replaced by a(au/at), studied in this paper, where the item au/at which makes it more general. The sufficient condition of the existence and uniqueness of non-trivial solution in L2(O, T; L2 (Ω)) is presented by employing the techniques of splitting the boundary problems into operator equation. Compared to the corresponding work, the restrictions imposed on the equation are weaken and the proof technique is simplified. It can be regarded as the extension and complement of the previous work.展开更多
This article is concerned with the weak convergence of invariant measures asso- ciated with multivalued stochastic differential equations in the finite dimensional space.
In this paper, We study a general class of nonlinear degenerated elliptic problems associated with the differential inclusion β(u)-div(α(x, Du)+F(u)) ∈ f in fΩ, where f ∈ L1 (Ω). A vector field a(.,....In this paper, We study a general class of nonlinear degenerated elliptic problems associated with the differential inclusion β(u)-div(α(x, Du)+F(u)) ∈ f in fΩ, where f ∈ L1 (Ω). A vector field a(.,.) is a Carath6odory function. Using truncation techniques and the generalized monotonicity method in the functional spaces we prove the existence of renormalized solutions for general L1-data. Under an additional strict monotonicity assumption uniqueness of the renormalized solution is established.展开更多
In this work, under global Lipschitz conditions, we prove the existence and uniqueness of strong solutions for multivalued stochastic McK ean-Vlasov equation. Moreover, under continuous and linear growth assumptions, ...In this work, under global Lipschitz conditions, we prove the existence and uniqueness of strong solutions for multivalued stochastic McK ean-Vlasov equation. Moreover, under continuous and linear growth assumptions, we also obtain the existence of weak solutions.展开更多
By using the perturbation theories on sums of ranges of nonlinear accretive mappings of Calvert and Gupta, we study the abstract results on the existence of a solution u ∈ L^s (Ω) of nonlinear boundary value probl...By using the perturbation theories on sums of ranges of nonlinear accretive mappings of Calvert and Gupta, we study the abstract results on the existence of a solution u ∈ L^s (Ω) of nonlinear boundary value problems involving the p-Laplacian operator, where 2≤ s〈+∞, and 2N/N+1 〈 p ≤ 2 for N(≥ 1) which denotes the dimension of R^N. To obtain the result, some new techniques are used in this paper. The equation discussed in this paper and our methods here are extension and complement to the corresponding results of L. Wei and Z. He.展开更多
By using some results of pseudo-monotone operator, we discuss the existence and uniqueness of the solution of one kind nonlinear Neumann boundary value problems involving the p-Laplacian operator. We also construct an...By using some results of pseudo-monotone operator, we discuss the existence and uniqueness of the solution of one kind nonlinear Neumann boundary value problems involving the p-Laplacian operator. We also construct an iterative scheme converging strongly to this solution.展开更多
The aim of the paper is to propose an iterative regularization method of proximal point type for finding a common solution for a finite family of inverse-strongly monotone equations in Hilbert spaces.
Matsushita, Takahashi[4] proved a strong convergence theorem for relatively nonex- pansive mappings in a Banach space by using the hybrid method (CQ method) in mathematical programming. The purpose of this paper is to...Matsushita, Takahashi[4] proved a strong convergence theorem for relatively nonex- pansive mappings in a Banach space by using the hybrid method (CQ method) in mathematical programming. The purpose of this paper is to modify the hybrid method of Matsushita, Taka- hashi by monotone CQ method, and to prove strong convergence theorems for weak relatively nonexpansive mappings and maximal monotone operators in Banach spaces. The convergence rate of monotone CQ method is faster than the hybrid method of Matsushi...展开更多
Using perturbation theories on sums of ranges of nonlinear accretive mappings of Calvert and Gupta, we present the abstract results on the existence of solutions of one kind nonlinear Neumann boundary value problems r...Using perturbation theories on sums of ranges of nonlinear accretive mappings of Calvert and Gupta, we present the abstract results on the existence of solutions of one kind nonlinear Neumann boundary value problems related to p-Laplacian operator. The equation discussed in this paper and the method used here extend and complement some of the previous work.展开更多
基金supported by the NSFC(12071413)the Guangxi Natural Sci-ence Foundation(2023GXNSFAA026085)the European Union's Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie grant agreement No.823731 CONMECH。
文摘We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation.We prove the existence theorems for both the convex and nonconvex problems.We also show the existence of extremal periodic solutions and provide a strong relaxation theorem.Finally,we provide an application to nonlinear periodic control systems.
基金the National Natural Science Foundation of China (10771050)
文摘In this paper, some iterative schemes for approximating the common element of the set of zero points of maximal monotone operators and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed. Some strong convergence theorems are obtained, to extend the previous work.
基金Supported by the National Natural Science Foundation of China
文摘A proximal iterative algorithm for the mulitivalue operator equation 0 ∈ T(x) is presented, where T is a maximal monotone operator. It is an improvement of the proximal point algorithm as well know. The convergence of the algorithm is discussed and all example is given.
基金Supported by the National Natural Science Foundation of China(10771050)the Natural Science Foun-dation of Hebei Province(A2010001482)
文摘In this paper, some new iterative schemes for approximating the common element of the set of fixed points of strongly relatively nonexpansive mappings and the set of zero points of maximal monotone operators in a real uniformly smooth and uniformly convex Banach space are proposed. Some weak convergence theorems are obtained, which extend and complement some previous work.
基金Supported both by the Teaching and Research Award Fund for Outstanding Young Teachers inHigher Educational Institutions of MOEChinaand by the Dawn Program Fund in Shanghai
文摘In order to find roots of maximal monotone operators, this paper introduces and studies the modified approximate proximal point algorithm with an error sequence {e k} such that || ek || \leqslant hk || xk - [(x)\tilde]k ||\left\| { e^k } \right\| \leqslant \eta _k \left\| { x^k - \tilde x^k } \right\| with ?k = 0¥ ( hk - 1 ) < + ¥\sum\limits_{k = 0}^\infty {\left( {\eta _k - 1} \right)} and infk \geqslant 0 hk = m\geqslant 1\mathop {\inf }\limits_{k \geqslant 0} \eta _k = \mu \geqslant 1 . Here, the restrictions on {η k} are very different from the ones on {η k}, given by He et al (Science in China Ser. A, 2002, 32 (11): 1026–1032.) that supk \geqslant 0 hk = v < 1\mathop {\sup }\limits_{k \geqslant 0} \eta _k = v . Moreover, the characteristic conditions of the convergence of the modified approximate proximal point algorithm are presented by virtue of the new technique very different from the ones given by He et al.
文摘By using the perturbation theories on sums of ranges for nonlinear accretive mappings of Calvert and Gupta (1978),the abstract result on the existence of a solution u ∈ L^p (Ω) to nonlinear equations involving p-Laplacian operator △p, where 2N/N+1〈p〈+∞ and N (≥ 1 ) denotes the dimension of R^N,is studied. The equation discussed and the methods shown in the paper are continuation and complement to the corresponding results of Li and Zhen's previous papers. To obtain the result ,some new techniques are used.
基金the National Natural Science Foundation of China (No. 10771050).
文摘In this paper, two iterative schemes for approximating common element of the set of zero points of maximal monotone operators and the set of fixed points of a kind of generalized nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed. Two strong convergence theorems are obtained and their applications on finding the minimizer of a kind of convex functional are discussed, which extend some previous work.
基金the National Natural Science Foundation of China (No.10771050)
文摘A new projection scheme with errors for zero points of maximal monotone operators is introduced and is proved to be strongly convergent to zero points of maximal monotone operators in Banach space by using the techniques of Lyapunov functional and generalized projection operator, etc.
文摘In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operators. We establish the existence and uniqueness ofanti-periodic solutions, which improve andgeneralize the results that have been obtained. Finally weillustrate the abstract theory by discussing a simple example of an anti-periodic problem fornonlinear partial differential equations.
文摘By using the perturbation results of sums of ranges of accretive mappings of Calvert and Gupta(1978),the abstract results on the existence of solutions of a family of nonlinear boundary value problems in L2(Ω) are studied.The equation discussed in this paper and the methods used here are extension and complement to the corresponding results of Wei Li and He Zhen's previous papers.Especially,some new techniques are used in this paper.
基金supported by the Natural Science Foundation of Yibin University (No. 2009Z003)
文摘This paper uses a hybrid algorithm to find a common element of the set of solutions to a generalized mixed equilibrium problem, the set of solutions to variational inequality problems, and the set of common fixed points for a finite family of quasi-C- nonexpansive mappings in a uniformly smooth and strictly convex Banach space. As applications, we utilize our results to study the optimization problem. It shows that our results improve and extend the corresponding results announced by many others recently.
基金supported by the National Natural Science Foundation of China(11071053)Natural Science Foundation of Hebei Province(A2014207010)+1 种基金Key Project of Science and Research of Hebei Educational Department(ZD2016024)Key Project of Science and Research of Hebei University of Economics and Business(2015KYZ03)
文摘One parabolic p-Laplacian-like differential equation with mixed boundaries is au/at in the corresponding studies is replaced by a(au/at), studied in this paper, where the item au/at which makes it more general. The sufficient condition of the existence and uniqueness of non-trivial solution in L2(O, T; L2 (Ω)) is presented by employing the techniques of splitting the boundary problems into operator equation. Compared to the corresponding work, the restrictions imposed on the equation are weaken and the proof technique is simplified. It can be regarded as the extension and complement of the previous work.
基金supported by NSFs of China(11471340 and 11461028)
文摘This article is concerned with the weak convergence of invariant measures asso- ciated with multivalued stochastic differential equations in the finite dimensional space.
文摘In this paper, We study a general class of nonlinear degenerated elliptic problems associated with the differential inclusion β(u)-div(α(x, Du)+F(u)) ∈ f in fΩ, where f ∈ L1 (Ω). A vector field a(.,.) is a Carath6odory function. Using truncation techniques and the generalized monotonicity method in the functional spaces we prove the existence of renormalized solutions for general L1-data. Under an additional strict monotonicity assumption uniqueness of the renormalized solution is established.
基金supported by the National Natural Science Foundation of China(11271294)
文摘In this work, under global Lipschitz conditions, we prove the existence and uniqueness of strong solutions for multivalued stochastic McK ean-Vlasov equation. Moreover, under continuous and linear growth assumptions, we also obtain the existence of weak solutions.
基金This research is supported by the National Natural Science Foundation of China(No. 10471033).
文摘By using the perturbation theories on sums of ranges of nonlinear accretive mappings of Calvert and Gupta, we study the abstract results on the existence of a solution u ∈ L^s (Ω) of nonlinear boundary value problems involving the p-Laplacian operator, where 2≤ s〈+∞, and 2N/N+1 〈 p ≤ 2 for N(≥ 1) which denotes the dimension of R^N. To obtain the result, some new techniques are used in this paper. The equation discussed in this paper and our methods here are extension and complement to the corresponding results of L. Wei and Z. He.
基金Supported by the National Natural Science Foundation of China (No. 11071053)the Natural Science Foundation of Hebei Province (No.A2010001482)the project of Science and Research of Hebei Education Department (the second round in 2010)
文摘By using some results of pseudo-monotone operator, we discuss the existence and uniqueness of the solution of one kind nonlinear Neumann boundary value problems involving the p-Laplacian operator. We also construct an iterative scheme converging strongly to this solution.
基金Supported by the Vietnamese Natural Foundation for Science and Technology Development 2009
文摘The aim of the paper is to propose an iterative regularization method of proximal point type for finding a common solution for a finite family of inverse-strongly monotone equations in Hilbert spaces.
基金the National Natural Science Foundation of China (No.10771050)
文摘Matsushita, Takahashi[4] proved a strong convergence theorem for relatively nonex- pansive mappings in a Banach space by using the hybrid method (CQ method) in mathematical programming. The purpose of this paper is to modify the hybrid method of Matsushita, Taka- hashi by monotone CQ method, and to prove strong convergence theorems for weak relatively nonexpansive mappings and maximal monotone operators in Banach spaces. The convergence rate of monotone CQ method is faster than the hybrid method of Matsushi...
基金Supported by the National Natural Science Foundation of China (Grant No.10771050)the Project of Science and Research of Hebei Education Department (Grant No.2009115)
文摘Using perturbation theories on sums of ranges of nonlinear accretive mappings of Calvert and Gupta, we present the abstract results on the existence of solutions of one kind nonlinear Neumann boundary value problems related to p-Laplacian operator. The equation discussed in this paper and the method used here extend and complement some of the previous work.